Abstract
Verification is a task to check whether a given quantum state is close to an ideal state or not. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for verifying ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of quantum circuits. We finally propose an adaptive test of stabilizers that enables the verification of all polynomial-time-generated hypergraph states, which include output states of the Bremner-Montanaro-Shepherd-type instantaneous quantum polynomial time (IQP) circuits. Importantly, we do not make any assumption that the identically and independently distributed copies of the same states are given: Our protocols work even if some highly complicated entanglement is created among copies in any artificial way. As applications, we consider the verification of the quantum computational supremacy demonstration with IQP models, and verifiable blind quantum computing.
- Received 2 October 2017
- Revised 9 February 2018
DOI:https://doi.org/10.1103/PhysRevX.8.021060
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computers can potentially solve problems that are very hard, if not impossible, for traditional digital computers to solve. However, the fragile quantum states generated in quantum-information-processing protocols are strongly susceptible to noise from the surrounding environment and device imperfections. This can lead to critical errors in computation, so the quantum states in these devices must be verified. In this paper, we provide protocols for verifying several types of quantum states using measurements of only single quantum bits (qubits).
Several verification protocols have been proposed previously. However, these protocols can be applied only to restricted classes of quantum states, or they assume that errors occur independently and identically among states. Conversely, our protocols can be used for any noise model—including highly artificial ones that generate entanglement among states—and can verify a wide variety of quantum states. One important example of these states, known as hypergraph states, is an output of a famous quantum computation model (the IQP model) that is known to exhibit quantum supremacy (a class of models that are not universal but are hard to efficiently simulate in classical computers).
Our protocol can be used to make existing cloud-quantum-computing protocols verifiable, which means that a client can check the correctness of a server’s quantum computing. With the advent of cloud quantum computing, and the recent active study of quantum supremacy driven by Google, IBM, etc., our new verification protocols should be useful in near-term realizations of quantum information processing.
